Physics

Nonlinear system

Mathematics

Structural engineering

Parametric statistics

Statistics

Engineering

Composite material

Shotcrete

Geotechnical engineering

Materials science

Layer (electronics)

Hardening (computing)

Quantum mechanics

Journal of Engineering Mechanics

Ignoring the shotcrete hardening property in tunnel design may lead to an overestimation of the bearing capacity of shotcrete liners and underestimation of tunnel convergence. However, accounting for this nonlinear hardening behavior of shotcrete in the tunnel analytical model is difficult because of the complexity of the mathematical derivation. This study aims to establish an analytical model to estimate the influence of the shotcrete hardening property on tunnel response. To overcome this challenge, the shotcrete hardening age was divided into several linear stages, and the corresponding equivalent Young's modulus in each stage was calculated. A unified time-dependent solution was then proposed for predicting tunnel displacement and shotcrete liner pressure, with the tunnel face advancing effect and the installation delay of the shotcrete liner taken into consideration. The proposed analytical solution was applied to the Rong Jiawan tunnel in China, and the general trend of the analytical results agreed with that of the field data. Finally, a comprehensive parametric investigation including the sensitivity of the division of shotcrete age, geostress, and shotcrete hardening model was conducted based on the analytical model, and some useful recommendations for tunnel design are presented. The outcomes of this research can support tunnel design in similar projects.

Analytical Approach to Estimating the Influence of Shotcrete Hardening Property on Tunnel Response